91Ó°ÊÓ

We are given an urn containing 15 red balls and 10 white balls . Five balls are selected. In how many ways can the 5 balls be drawn from the total of 25 balls if all 5 balls are red?

We know that we have a total of 15 red balls and 10 white ball .The ways to draw 5 red balls is :

$C(15,5)=\frac{15!}{5!10!}$

$\frac{15×14×13×12×11×10!}{5×4×3×2×1×10!}=\frac{15×14×13×12×11}{5×4×3×2×1}$

$3×7×13×11=3003$ways

We are given an urn containing 15 red balls and 10 white balls . Five balls are selected. In how many ways can the 5 balls be drawn from the total of 25 balls if 3 balls are red and 2 are white?

We know that we have a total of 15 red balls and 10 white ball .The ways to draw 3 red balls and 2 white balls is :

$C(15,3)×C(10,2)=\frac{15!}{3!12!}×\frac{10!}{2!8!}$

$\frac{15×14×13×12!}{3×2×1×12!}×\frac{10×9×8!}{2×1×8!}=\frac{15×14×13}{3×2×1}×\frac{10×9}{2}$

$5×7×13×5×9=20475$ways

We are given an urn containing 15 red balls and 10 white balls . Five balls are selected. In how many ways can the 5 balls be drawn from the total of 25 balls if at least 4 balls are red?

We know that we have a total of 15 red balls and 10 white ball .The ways to draw at least 4 red balls is :

$C(15,4)×C(10,1)×C(11,1)=\frac{15!}{4!11!}×\frac{10!}{1!9!}×\frac{11!}{1!10!}$

$\frac{15×14×13×12×11!}{4×3×2×1×11!}×\frac{10×9!}{1×9!}×\frac{11×10!}{1×10!}=\frac{15×14×13×12}{4×3×2×1}×10×11$

$15×7×13×10×11=150150$ways